Known injection units of this type are generally actuated by a cam shaft mounted in the engine cylinder head, the pump piston being rotatable by means of a toothed control rod engaging in a gear of the pump piston for adjusting the displacement. As soon as the control edge provided at the piston end face has passed the mouth of the fuel passage and has thus enclosed the fuel in the cylinder in front of the piston end face, after a corresponding pressure rise, fuel discharge begins from the injection nozzle. If the rear control edge formed by a step in the piston running surface and connected to the piston end face via a passage formed as a groove or the like then frees the mouth of the fuel passage after further piston travel, the fuel discharge from the nozzle is terminated and the fuel conducted into the passage.